Zeroth Order Nonconvex Multi-Agent Optimization over Networks
This addresses distributed optimization in non-convex settings with limited information access, which is incremental as it extends existing convex methods to more complex scenarios.
The paper tackles distributed optimization for non-convex problems over multi-agent networks, where agents only access zeroth-order information, and develops algorithms with proven convergence rates to stationary solutions.
In this paper, we consider distributed optimization problems over a multi-agent network, where each agent can only partially evaluate the objective function, and it is allowed to exchange messages with its immediate neighbors. Differently from all existing works on distributed optimization, our focus is given to optimizing a class of non-convex problems, and under the challenging setting where each agent can only access the zeroth-order information (i.e., the functional values) of its local functions. For different types of network topologies such as undirected connected networks or star networks, we develop efficient distributed algorithms and rigorously analyze their convergence and rate of convergence (to the set of stationary solutions). Numerical results are provided to demonstrate the efficiency of the proposed algorithms.